{"id":"cb_question_bank:1201ba81-051c-4e6b-915d-400100ae655f","source_id":"cb_question_bank","source_item_id":"1201ba81-051c-4e6b-915d-400100ae655f","external_id":null,"ibn":"025483-DC","question_id":"42c71eb5","program":"SAT","module":"math","domain_code":"P","domain":"Advanced Math","skill_code":"P.A.","skill":"Equivalent expressions","difficulty":"M","score_band":5,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"Which of the following is equivalent to the expression above?","stimulus":"open parenthesis, 2 x plus 5, close parenthesis, squared, minus, open parenthesis, x minus 2, close parenthesis, plus 2 times, open parenthesis, x plus 3, close parenthesis","stimulus_html":"<div class=\"stimulus_reference \">\n        <p class=\"standalone_statement style:1 \">\n          <span class=\"math_expression \">\n            <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/b10b4fa7a491da72b2f6eb8557994e04019bb599463048caaded2468631e01ff\" alt=\"open parenthesis, 2 x plus 5, close parenthesis, squared, minus, open parenthesis, x minus 2, close parenthesis, plus 2 times, open parenthesis, x plus 3, close parenthesis\"></span></span>\n        </p>\n      </div>\n","stem_html":"<p class=\"stem_paragraph \">Which of the following is equivalent to the expression above?</p>\n","rationale_html":"<p>Choice A is correct. The given expression can be rewritten as <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/bf4c5f140c875154d36583d6ebfc7df0cfa2d33ff79c091bd750889b69d78b3f\" alt=\"open parenthesis, 2 x plus 5, close parenthesis, squared, plus, negative 1 times, open parenthesis, x minus 2, close parenthesis, plus, 2 times, open parenthesis, x plus 3, close parenthesis\"></span>. Applying the distributive property, the expression&nbsp; <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/cf50dae386827e290c59708c5eabd1e39e48fe4ceb7bf4724063f8a4b911cf39\" alt=\"negative 1 times, open parenthesis, x minus 2, close parenthesis, plus, 2 times, open parenthesis, x plus 3, close parenthesis\"></span>can be rewritten as <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/e5664468817191991034abb11c5b8432adf69a308051529e39a2af80198e07a6\" alt=\"negative one times x, plus, negative 1 times negative 2, plus, 2 times x, plus, 2 times 3\"></span>, or <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/ca2cfab2e631f54c7f0ea786c0e8ad98c5cded4877d7536d3c63386da9a37f09\" alt=\"negative x plus 2, plus 2 x, plus 6\"></span>. Adding like terms yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/73485bf969dab4fd90d72e88c8febbfac08c63f58f7e663a186733b5903891f9\" alt=\"x plus 8\"></span>. Substituting <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/73485bf969dab4fd90d72e88c8febbfac08c63f58f7e663a186733b5903891f9\" alt=\"x plus 8\"></span> for&nbsp; <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/cf50dae386827e290c59708c5eabd1e39e48fe4ceb7bf4724063f8a4b911cf39\" alt=\"negative 1, times, open parenthesis, x minus 2, close parenthesis, plus, 2 times, open parenthesis, x plus 3, close parenthesis\"></span> in the given expression yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/4a2a358c733c1c22d4c24f122674fc533a2964adf4203cd18d65800ed64f26aa\" alt=\"open parenthesis, 2 x plus 5, close parenthesis, squared, plus x, plus 8\"></span>. By the rules of exponents, the expression <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/a3ea93a6f49b2e88ba82877eead11b175e98bee4b7b016c39899fc101816c696\" alt=\"open parenthesis, 2 x plus 5, close parenthesis, squared \"></span> is equivalent to <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/2ab097fd91dca39e52c02fb03265ac55f68647dbf7d9106b1fd9d1b5aee9892c\" alt=\"open parenthesis, 2 x plus 5, close parenthesis, times, open parenthesis, 2 x plus 5, close parenthesis\"></span>. Applying the distributive property, this expression can be rewritten as <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/8c4d546735a47ad52963b339e6ac2f5cb1240a3613b67b1038324f4c3716f233\" alt=\"2 x times 2x, plus, 2 x times 5, plus, 5 times 2 x, plus, 5 times 5\"></span>, or <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/34cd68d9e04e482dc9aa271a0120166524e80b2aa21b95d6fbb5309ff5a0bd7a\" alt=\"4 x squared, plus 10 x, plus 10 x, plus 25\"></span>. Adding like terms gives <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/315c9c0ae5d7d375e3b2605dd556711bec8a98397daba668aeb6afbe351535fe\" alt=\"4 x squared, plus 20 x, plus 25\"></span>. Substituting <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/315c9c0ae5d7d375e3b2605dd556711bec8a98397daba668aeb6afbe351535fe\" alt=\"4 x squared, plus 20 x, plus 25\"></span> for <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/a3ea93a6f49b2e88ba82877eead11b175e98bee4b7b016c39899fc101816c696\" alt=\"open parenthesis, 2 x plus 5, close parenthesis, squared\"></span> in the rewritten expression yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/91551f8361c3c4b752521fbe9b23129b4fc16d734c4d03b7114c11da10111d31\" alt=\"4 x squared, plus 20 x, plus 25, plus x, plus 8\"></span>, and adding like terms yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/0feb6b503af357f30c5acc836b94d3a3ecec369cacf551d6db0d1355408e58d9\" alt=\"4 x squared, plus 21 x, plus 33\"></span>.</p><p>Choices B, C, and D are incorrect. Choices C and D may result from rewriting the expression <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/2f837ecc55d8e8fa40605eaad37e99d47119bb0c153c3368838451fdfd514550\" alt=\"open parenthesis, 2 x plus 5, close parenthesis, squared \"></span> as <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/7f03287934ac9504447e04414190c2faff5e843967f1d8a8b99547d77b886936\" alt=\"4 x squared, plus 25\"></span>, instead of as <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/315c9c0ae5d7d375e3b2605dd556711bec8a98397daba668aeb6afbe351535fe\" alt=\"4 x squared, plus 20 x, plus 25\"></span>. Choices B and C may result from rewriting the expression <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/41f3be2e833871edeee0edb8aac0b69fb24cb8522bdd9223e90a8cf7c9989ffc\" alt=\"negative, open parenthesis, x minus 2, close parenthesis\"></span> as <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/171c5312d536eb8fa7a30070f06b296f860ec24ecafa3863a9f65601063d320d\" alt=\"negative x minus 2\"></span>, instead of <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/63e7fbd48df31456740ed372192c0fb4048aa766e944041af3f3964195b440d1\" alt=\"negative x plus 2\"></span>.</p><p></p>\n","correct_answer":["A"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.619000+00:00","source_updated_at":"2023-08-02T20:25:59.619000+00:00","options":[{"label":"A","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"math_expression \">\n              <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/0feb6b503af357f30c5acc836b94d3a3ecec369cacf551d6db0d1355408e58d9\" alt=\"4 x squared, plus 21 x, plus 33\"></span></span>\n          </p>\n","ord":0},{"label":"B","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"math_expression \">\n              <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/d822dc088a5d2eecbb6b9319b3db743af628a7ad2451b49b4c1ff5afe7f18cb0\" alt=\"4 x squared, plus 21 x, plus 29\"></span></span>\n          </p>\n","ord":1},{"label":"C","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"math_expression \">\n              <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/85032795909279970f051a791f9e97af31223c26875182663444ac973f093896\" alt=\"4 x squared, plus x, plus 29\"></span></span>\n          </p>\n","ord":2},{"label":"D","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"math_expression \">\n              <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/ee6e7df3172d6be5b36a675ca823872bab2bf97231199d3dbe017402bc95c3a3\" alt=\"4 x squared, plus x, plus 33\"></span></span>\n          </p>\n","ord":3}],"attribution":{"source_id":"cb_question_bank","source_name":"College Board digital SAT question bank (community dump)","rights_holder":"College Board","canonical_url":"https://satsuitequestionbank.collegeboard.org/","retrieved_from":"https://raw.githubusercontent.com/mdn522/sat-question-bank/main/data/cb-digital-questions.json","attribution":"SAT practice questions © College Board, from the official SAT Suite Question Bank. Retrieved via the community dump at github.com/mdn522/sat-question-bank.","disclaimer":"SAT® and PSAT/NMSQT® are trademarks registered by the College Board, which is not affiliated with, does not sponsor, and does not endorse this project.","license":"College Board copyright; source repository carries no licence. Local use only.","redistributable":false,"item_count":2017}}